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The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ________.

$\begin{array}{1 1}(A)\;0.2\\(B)\;0.3\\(C)\;0.4\\(D)\;0.6\end{array} $

1 Answer

  • $P(A \cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
A and B are mutually exclusive events.
$\therefore P(A\cap B)=\phi=0$
Step 2:
$P(A \cup B)=P(A)+P(B)-P(A\cap B)$
$\Rightarrow 0.5+0.3$
$\Rightarrow 0.8$
$P(A \cup B)'=1-P(A \cup B)$
$\Rightarrow 1-0.8$
$\Rightarrow 0.2$
Hence (A) is the correct answer.
answered Jul 9, 2014 by sreemathi.v